How to get around triangles?
Personally, I don't trust the knife tool unless it's to do something very specific. It can make lots of irregular faces if used as a freehand tool. I'd rather stick to loopcuts and not worry about the extra faces.

Judging from your second screenshot, seems like you're trying to make some kind of piece/emblem from your current mesh (which is starting to look pretty weird). I'd recommend to make that part as a different object and then join or parent to your first object.